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Full text of "Mathematical And Physical Papers - Iii"

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resulting in the value of r, or rather the corresponding error in the calculated value of n or k, might just have been sensible. The fifth column in the above table is copied from Baily's table. The next contains a small correction necessary to reduce the value of tt got from observation to what would have been got from observations made in an unlimited mass of fluid. It is calculated from the formula 2&2 (bz  a2)'1 or 2&26~2 nearly, which is obtained from the ordinary equations of hydrodynamics, and therefore it cannot be regarded as more than a rude approximation. It will be useful, however, as affording an estimate of the magnitude of the effect produced by confining the air. The diameter of the vacuum tube (whether external or internal is not specified) is stated to have been six inches and a half, whence 26 = 6*5. The values of k given in the next column are obtained by applying the correction for confined space to Baily's values of n, and subtracting unity. The value of in corresponding to each value of k was got by interpolation from the table near the end of Section III. of the former part of this paper. For &= 1*923 the interpolation is easy. The value 3*081 happens to be almost exactly found in the table. For k = 6*530, a remark already made will be found to be of importance, namely, that the first differences of m2(&  1) are nearly constant. The last column contains the value of \jp obtained from the equation
which contains the definition of ttl.
It will be observed that the three values of *Jp are nearly identical. Of course any theory professing to account for a set of experiments by means of a particular value of a disposable constant, when applied to the experiments would lead to nearly the same numerical value of the constant if the experiments were made under nearly the same circumstances. But in the present case the circumstances of the experiments are widely different. The diameter of the steel rod is little more than the sixth part of that of the copper rod, and the value of k obtained by experiment for the steel rod is more than three times as great as that obtained for the copper rod. It is a simple consequence of the ordinary theory of hydrodynamics that in the case of a long rod oscillating